Related papers: Block Permutation Routing on Ramanujan Hypergraphs…
The packet routing problem plays an essential role in communication networks. It involves how to transfer data from some origins to some destinations within a reasonable amount of time. In the $(\ell,k)$-routing problem, each node can send…
Block coordinate descent is an optimization paradigm that iteratively updates one block of variables at a time, making it quite amenable to big data applications due to its scalability and performance. Its convergence behavior has been…
Blockmodeling of a given problem represented by an $N\times N$ adjacency matrix can be found by swapping rows and columns of the matrix (i.e. multiplying matrix from left and right by a permutation matrix). Although classical matrix…
We investigate spectral fluctuations in multilayer networks within the random matrix theory (RMT) framework to characterize universal and non-universal features. The adjacency matrix of a multilayer network exhibits a block structure, with…
We introduce a construction for protocols for fault-tolerant quantum computing based on code concatenation and transversal gates. These protocols can be interpreted as families of quantum circuits of low-weight stabilizer measurements…
Permutation-based metaheuristics are widely used for electric vehicle routing, where candidate solutions are represented as ordered sequences of customers. Such sequences, however, do not directly define feasible vehicle routes: they must…
This is the first of two complementary works in which we analyze the connected components of the degree-corrected stochastic block model (DCSBM). Our model is a random graph with an underlying community structure and degree in-homogeneity.…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
Quantum low-density parity-check codes reduce quantum error correction overhead but require dense, long-range connectivity that challenges hardware implementation, particularly for superconducting processors. We address this problem by…
HyperSurfaces (HSFs) consist of structurally reconfigurable metasurfaces whose electromagnetic properties can be changed via a software interface, using an embedded miniaturized network of controllers. With the HSF controllers,…
For quantum error-correcting codes to be realizable, it is important that the qubits subject to the code constraints exhibit some form of limited connectivity. The works of Bravyi & Terhal (BT) and Bravyi, Poulin & Terhal (BPT) established…
Quantum error-correcting codes with asymptotically lower overheads than the surface code require nonlocal connectivity. Leveraging multilayer routing and long-range coupling capabilities in superconducting qubit hardware, we develop…
We prove that a random $d$-regular graph, with high probability, is a cut sparsifier of the clique with approximation error at most $\left(2\sqrt{\frac 2 \pi} + o_{n,d}(1)\right)/\sqrt d$, where $2\sqrt{\frac 2 \pi} = 1.595\ldots$ and…
Limited connectivity makes nonlocal quantum gates expensive on near-neighbor hardware, where compilation typically relies on SWAP transport, inheriting both depth overhead and path congestion. We present a swap-free routing framework in…
In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small…
Given a distributed network represented by a weighted undirected graph $G=(V,E)$ on $n$ vertices, and a parameter $k$, we devise a distributed algorithm that computes a routing scheme in $(n^{1/2+1/k}+D)\cdot n^{o(1)}$ rounds, where $D$ is…
We formulate a global-position colored-permutation encoding for the capacitated vehicle routing problem. Each of the $K$ vehicles selects a disjoint partial permutation, and the sum of these $K$ color layers forms a full $n\times n$…
Over the past 50 years, conventional network routing design has undergone substantial growth, evolving from small networks with static nodes to large systems connecting billions of devices. This progress has been achieved through the…
We present a succinct data structure for permutation graphs, and their superclass of circular permutation graphs, i.e., data structures using optimal space up to lower order terms. Unlike concurrent work on circle graphs (Acan et al. 2022),…
Oblivious routing has a long history in both the theory and practice of networking. In this work we initiate the formal study of oblivious routing in the context of reconfigurable networks, a new architecture that has recently come to the…